Thermography is an imaging technique based on infrared emission by an object at a particular temperature (grey body radiation). Thermography may include passive thermography or active thermography. Active Thermography is defined as applying a stimulus to a target to cause the target to heat or cool in such a way as to allow characteristics of the target to be observed when viewed by thermal imagery. Active thermography plays a crucial role as a non-destructive technique in many industries, especially in aerospace. Electromagnetic excitation is the most commonly used way of exciting the sample among thermo graphic techniques.
Thermography may also be classified as point imaging thermography, line imaging thermography, area imaging thermography and three-dimensional (3D) imaging thermography (tomography). Area or 3D imaging thermography may also be classified as one-sided or two-sided thermography. Active area imaging thermography may include a detector such as an infrared camera, a heating source as well as image processing software. FIG. 1 is a schematic 100a showing a one-sided optically excited thermography system. A flash lamp 104 is used as a source of electromagnetic radiation to illuminate a surface of sample 102. The infrared camera 106 is used to record the temperature evolution of the sample surface. The source 102 and the detector 106 are arranged on the same side in relation to the sample 104 in one-sided optically excited thermography. The camera 106 and the flash lamp 102 may be coupled to a computer 108. The computer 108 may be configured to acquire data from the camera 106 as well as configured to control the camera 106 and flash lamp 102.
FIG. 2 is a schematic 200a showing a two-sided optically excited thermography system. An infrared radiator or heating lamp 202 is used as a source of electromagnetic radiation to illuminate a sample 204. The infrared camera 206 is arranged at the side (of the sample 204) opposite the radiator 202 to record the temperature evolution. The source 202 and the detector 206 may be arranged on opposite sides in relation to the sample 204 in two-sided optically excited thermography. The camera 206 may be coupled to a computer 208.
The lamp radiator 104, 204 may be a tungsten filament lamp with broad spectral response but in general, alternative sources with spectral components from UV to microwave have been utilized by different groups. This technique has been particularly successful in finding delaminations in Fiber Reinforced Plastics (FRP). The thermo-physical properties of such defects display a high contrast to the fibers and matrix of FRP. Such substantial contrasts allow the lateral conduction in the FRP to be disregarded and heat propagation within the sample be treated as a one dimensional (1D) problem, making it possible to extract depth information from the thermography data. However, for defects with much lower contrast, the effectiveness of active thermography may drop dramatically.
One sided active thermography (shown in FIG. 1) heavily relies on the one-dimensional (1D) approximation of heat diffusion into the semi-infinite sample for processing the acquired data. For the case of semi-infinite solid, the solution may be analytically defined through the dimensional analysis depending on the boundary condition at the surface. For the most common approach, the instantaneous plane Dirac heat source is assumed, which is implemented through application of flash lamps. In this case, the solution for temperature T(α,z,t,Q′) for t>0 is a function of material diffusivity (α) in [m2/s], depth (z) in [m], time (t) in [s], and energy density Q′ that the surface was subjected to. Q′ may be defined as follows:Q′=Q/ρcpA  (1)where Q is the energy, ρ is the density of the sample, A is the surface area and cp is the specific heat capacity of the sample in [J/kgK].
Among all these variables only Q′ has unit of temperature in it, i.e.[Q′]=[m]*[K] (meter-Kelvin)  (2)As other units cannot remove temperature dependence, Q′ cannot be used as part of any dimensionless variable of exponential or trigonometric function in the solution. Hence, only α, z, and t remain. The only dimensionless combination that can be formed from these parameters is z/√(αt). In order to satisfy the dimensions of temperature the solution should depend on either q/z or q/√(αt). In our case only the second variant makes sense for t>0 and z=0. Hence, the solution should have a form of
                              T          =                                                    Q                ′                                                              α                  ⁢                                                                          ⁢                  t                                                      ⁢                          U              ⁡                              (                η                )                                                    ⁢                                  ⁢        where                            (        3        )                                η        =                  z                                    α              ⁢                                                          ⁢              t                                                          (        4        )            
Looking at partial differentiation by z and t of this function,
                                          ∂            T                                ∂            t                          =                                            dT                              d                ⁢                                                                  ⁢                η                                      ⁢                                          ∂                η                                            ∂                t                                              =                                    -                              z                                  2                  ⁢                  t                  ⁢                                                            α                      ⁢                                                                                          ⁢                      t                                                                                            ⁢                          dT                              d                ⁢                                                                  ⁢                η                                                                        (        5        )                                                      ∂            T                                ∂            z                          =                                            dT                              d                ⁢                                                                  ⁢                η                                      ⁢                                          ∂                η                                            ∂                z                                              =                                    -                              1                                                      α                    ⁢                                                                                  ⁢                    t                                                                        ⁢                          dT                              d                ⁢                                                                  ⁢                η                                                                        (        6        )                                                                    ∂              2                        ⁢            T                                ∂                          z              2                                      =                                            d                              d                ⁢                                                                  ⁢                η                                      ⁢                          (                                                ∂                  T                                                  ∂                  z                                            )                        ⁢                                          ∂                η                                            ∂                z                                              =                                    1                              α                ⁢                                                                  ⁢                t                                      ⁢                                                            d                  2                                ⁢                T                                            d                ⁢                                                                  ⁢                                  η                  2                                                                                        (        7        )            
The implications of these transformation is that the partial differential equations for heat diffusion become an ordinary differential equation as follows:
                                                        d              2                        ⁢            T                                d            ⁢                                                  ⁢                          η              2                                      =                              -            2                    ⁢          η          ⁢                      dT                          d              ⁢                                                          ⁢              η                                                          (        8        )            
The implication is that from the projection of temperature evolution at the surface (z=0), one can directly reconstruct the depth distribution at each value of z. Hence, if the measured result deviates form the solution for the semi-infinite body due to the presence of a defect, the time of the onset of deviation may be directly translated into the depth of the defect. However, deviation from 1D model can also happen due to 3D diffusion and the proposed approximation is invalid. For 3D heat diffusion to be ignored one or several of the following criteria should to be satisfied:
1) The surface heating is uniform, so that there are no lateral gradients.
2) The contrast in thermo-physical parameters between defect and sound regions of the sample is high enough to create temperature gradients much larger in comparison with deviation from one dimensional (1D) solution.
3) The detection is performed shortly after the heat source is switched off, so that heat diffusion is minimal. Similarly this criterion can be defined if the location of the defect is close to the surface.
In all other conditions the estimation of z may be grossly inaccurate.
The most common method for heating the surface in active thermography is to use halogen lamps. The illumination with such lamps is inherently non-uniform due to lamp geometry. It is possible to achieve a limited relatively uniform area on the sample surface if 2 or more lamps are implemented simultaneously. However, it dramatically increases the complexity and cost of the system. Due to limited area of uniformity, even for such complex system, the lateral conduction may eventually kick in. At the same time, even if the perfectly uniform illumination can be achieved, it may not guarantee the uniform heat transfer to the surface. Sample and set-up geometry may affect the incidence angle of the light form the lamp, which can have very strong effect on absorption efficiency. Absorption efficiency may also be affected by surface contamination, microstructure or semi-transparency of the top layers. All these effects on absorption efficiency may create localized lateral temperature gradients, which will make the 1D approximation poorly suitable in those locations. These gradients may often disappear in a short period of time if lateral conductivities are high enough. However, at longer periods, the third criterion may not be satisfied. In most cases, active thermography may be implemented when the second criterion is imposed, which means that the contrast in thermo-physical parameters between defect and sample may be much higher than the effects due to 3D diffusion.
The limitations of the conventional active thermography based on flash lamps may be summarized in a following manner:
1) It may be challenging to achieve uniform illumination of the material, which introduces lateral temperature gradients that will dominate the IR image.
2) Even if the uniformity of illumination can be achieved, it may be practically impossible to avoid variation of the light absorption at the surface, which may depend on material composition, surface structure and finishing and presence of surface contamination.
3) Even after the flash is applied, the glow from the lamp may stay strong for several seconds and may be reflected from the sample into the camera. This may not make it possible to use the thermography at early stages of thermal transition.
4) Application in ambient condition may cause cooling of the surface through convection, which may contributes quite a lot after 10 seconds of observation.
All these issues may limit application of active thermography only to the defects with high contrast in thermo-physical parameters in relation to base material under inspection.